Download Name:_________________________ Date:________ Radical Expressions and Functions

Name:_________________________
Date:________
Practice Set 7.1
Radical Expressions and Functions
Evaluate each expression or state that the expression is not a real number.
1.
16 =
1. _______________
2.
3
x3 =
2. _______________
3.
4
81 =
3. _______________
64 =
4. _______________
4.
5.
3
1
=
8
5. _______________
6.
3
y6 =
6. _______________
7.
3
64 =
7. _______________
8.
3
−1 =
8. _______________
9.
– 64 =
9. _______________
10.
196 =
10. _______________
79
Name:_________________________
Date:________
Find the function values for each function. If the function value is not a real number, so state.
11.
f ( x ) = 15 − x
Find
12.
11a. ______________
b. f (0)
b. ______________
c. f (19)
c. ______________
g ( x) = 2 x + 5
Find
13.
a. f (6)
a. g(4)
12a. ______________
b. g (–3)
b. ______________
c. g (–2)
c. ______________
h( x) = x 2 − 1
Find
a. h(4)
13a ______________
b. h(0)
b. ______________
c. h(1)
c. ______________
Find the domain of each square root function.
14.
f ( x) =
x−6
14. ______________
15.
g ( x) = 10 − x
15. ______________
16.
h( x) = 2 x + 2
16. ______________
80
Name:_________________________
Date:________
Practice Set 7.2
Rational Exponents
Rewrite each exponential expression as an equivalent radical expression. Simplify if possible.
1.
2.
17
81
1
3
1. _______________
3
4
2. _______________
1
2
3.
16
4.
(–8) 3
3. _______________
2
5.
4. _______________
1
3 3
(125 x )
5. _______________
Rewrite each radical expression as an exponential expression.
6.
3
7.
8.
5
10 4
6. _______________
25
7. _______________
x8
8. _______________
9.
( 12xy )
9. _______________
10.
16 x
10. _______________
7
3
81
Name:_________________________
Date:________
Simplify.
2
11.
(3 3 ) 3
1
3
11. _______________
1
6
12.
a ⋅a
13.
16
14.
2 2 ⋅ 2 −4
−
12. _______________
1
4
13. _______________
14. _______________
1
2
15.
49
16.
(–8) 3
15. _______________
1
17.
4
4
18.
3
16. _______________
5
6
17. _______________
2
6
− 216
18. _______________
−2
3
19.
27
20.
(32 )
19. _______________
1
3 5
20. _______________
82
Name:_________________________
Date:________
Practice Set 7.3
Multiplying and Simplifying Radical Expressions
Simplify each radical. Assume that all variables in a radicand represent positive real numbers.
1.
45
1. _______________
2.
600
2. _______________
3.
18x 2
3. _______________
4.
2 ⋅ 20
4. _______________
5.
5 ⋅ 15
5. _______________
6.
x 6 y 10
6. _______________
7.
a 9 b16
7. _______________
27 x 6 y 12
8. _______________
9.
80a 4 b 3 c 2
9. _______________
10.
x4 y7 z
10. _______________
6x ⋅ 3 4x 2
11. _______________
5a ⋅ 10ab
12. _______________
8.
11.
3
3
12.
13.
3
2 ⋅ 3 20
13. _______________
14.
5
− 32 x 6 y 3
14. _______________
15.
4
9 x 3 y 3 ⋅ 4 9 x 5y 9
15. _______________
16.
3 6 ⋅2 2
16. _______________
17.
5 5 ⋅5 5
17. _______________
83
Name:_________________________
Date:________
84
Name:_________________________
Date:________
Practice Set 7.4
Adding, Subtracting, and Dividing Radical Expressions
Add, subtract or divide, if possible. If not possible, state why it is not possible. Assume all
variables are positive. Answers must be in simplified form.
1.
5 6 +3 6
1. _______________
2.
8 3+ 3+2 3
2. _______________
3.
4 20 – 2 5
3. _______________
4.
3 32 x 2 + 5 x 8
4. _______________
5.
10 2 – 5 4 + 8 8
5. _______________
6.
200 + 72 + 50
6. _______________
7.
5 7x2 + 3 7
7. _______________
8.
7 4 x + 2 25 x + 3 16 x
8. _______________
9.
10.
14 x
9. _______________
7x
50 x 3 y 4
2 xy
10. _______________
85
Name:_________________________
Date:________
11.
3 y 27 x 5 y + 2 x 3 x 3 y 3
11. _______________
12.
10 50a 4 – 5a 98a 2
12. _______________
13.
3
14.
18 9 y 3 – 12 y 16 y + 2 25 y 3
14. _______________
15.
15 12 – 3 12 + 12
15. _______________
16.
4
17.
73 a 4b3c 2 – 6ab3 ac 2
17. _______________
18.
4 18 x 2 y – 3 x 50 y
18. _______________
19.
5
64 y 7
2y2
3
40 a 6 b 4
20.
16 y 4
2y
13. _______________
32 y 4
2 y4
3
16. _______________
19. _______________
20. _______________
5b
86
Name:_________________________
Date:________
Practice Set 7.5
Multiplying With More Than One Term and Rationalize
Multiply and simplify.
1.
3(x – 6 )
1. _______________
2.
2 (3 3 – 2 2 )
2. _______________
3.
(6 + 2 )(3 – 2 )
3. _______________
4.
( 5 + 7)( 2 5 – 3 7 )
4. _______________
5.
(2 3 – 5 7 ) 2
5. _______________
6.
(2 6 − 3 ) 2
6. _______________
7.
( 4 + 2 5 )(4 – 2 5 )
7. _______________
8.
( x – 4)( x + 4)
8. _______________
Simplify each radical expression and then rationalize the denominator.
9.
10.
11.
3
6
5
9. _______________
2
5
10. _______________
4
3y
11. _______________
87
Name:_________________________
12.
3
4
25
3
13.
3
4
16.
17.
18.
12. _______________
2
13. _______________
3y 2
3
14.
15.
Date:________
14. _______________
x3 y
9
15. _______________
5– 2
6 3
3 –1
16. _______________
5– 2
17. _______________
5+ 3
3 2+2 5
18. _______________
5 3+4 2
88
Name:_________________________
Date:________
Practice Set 7.6
Radical Equations
Solve each radical equation.
1.
x – 3 =1
1. _______________
2.
2x – 6 = 8
2. _______________
x−5 = 2
3. _______________
4.
3 x + 4 = −10
4. _______________
5.
2x − 3 − 2 = 1
5. _______________
6.
x – 5 − 6 = –3
6. _______________
x + 3 − 9 = −8
7. _______________
3x + 1 + 4 = 2
8. _______________
3.
7.
3
4
8.
1
2
9.
(4a + 5) + 7 = 12
9. _______________
10.
3
3y − 7 + 4 = 6
10. _______________
11.
( a + 4) 4 = 2
1
y + 14 = y + 2
12.
13.
12. _______________
2 4 x + 5 = 14
14.
15.
11. _______________
3
13. _______________
x + 3 = 3x + 9
14. _______________
4x + 9 = 3 3 − 2x
15. _______________
1
1
16.
(2 y + 5) 2 = (5 y + 2) 2
16. _______________
17.
x+8 = x−4 +2
17. _______________
1
18.
(8 − 3 x) 3 = −1
18. _______________
89
Name:_________________________
Date:________
90
Name:_________________________
Date:________
Practice Set 7.7
Complex Numbers
Simplify.
1.
– 32
1. _______________
2.
−1
2. _______________
3.
8 − − 25
3. _______________
4.
– − 75
4. _______________
Add, subtract, multiply or divide. Simplify if possible. Answers should be in the form a + bi if
possible.
5.
( 4 + 3i ) + (3 + i )
5. _______________
6.
(6 − 2i ) − ( 4 − 5i )
6. _______________
7.
3i − (5 − 7i )
7. _______________
8.
− 25 ⋅ − 4
8. _______________
9.
2i (5 − 3i )
9. _______________
10.
( 2 + i )( 2 − i )
10. _______________
11.
− 4i ⋅ 4i
11. _______________
12.
( 2 + i 3 )( 2 − i 3 )
12. _______________
91
Name:_________________________
Date:________
13.
( 4 + 2i ) − (3 − 6i )
13. _______________
14.
2 + 3i
i
14. _______________
15.
4
2 + 3i
15. _______________
16.
− 6i ( 2 + i )
16. _______________
17.
(4 − 3i ) 2
17. _______________
18.
2+i
5 − 6i
18. _______________
19.
(5 − 2i )(1 + i )
19. _______________
20.
4 + 3i
3 + 6i
20. _______________
Simplify
21.
i 40
21. _______________
22.
i 34
22. _______________
23.
i 120
23. _______________
24.
i 63
24. _______________
25.
i 17
25. _______________
92